Question 1

1. A tangent to a circle intersects the circle in exactly how many points?

A) 1B) 2C) 3D) Infinite

Answer

✓ Correct Answer: Option A

Question 2

2. A line intersecting a circle in two distinct points is called a:

A) TangentB) SecantC) ChordD) Diameter

Answer

✓ Correct Answer: Option B

Question 3

Question 4

4. The common point of a tangent to a circle and the circle itself is called the:

A) Point of contactB) CenterC) Point of intersectionD) Exterior point

Answer

✓ Correct Answer: Option A

Question 5

5. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. What is the radius of the circle?

A) 2 cmB) 3 cmC) 6 cmD) $\sqrt{41} cm$

Answer

✓ Correct Answer: Option B

Question 6

6. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^\circ$, then \angle POA is equal to:

A) $50^\circ$B) $60^\circ$C) $70^\circ$D) $80^\circ$

Answer

✓ Correct Answer: Option A

Question 7

7. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is:

A) 7 cmB) 12 cmC) 15 cmD) 24.5 cm

Answer

✓ Correct Answer: Option A

Question 8

8. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

A) 4 cmB) 5 cmC) 8 cmD) 10 cm

Answer

✓ Correct Answer: Option C

Question 9

9. A quadrilateral ABCD is drawn to circumscribe a circle. Which of the following relations is always true?

A) AB + BC = CD + ADB) $AB \times CD = BC \times AD$C) AB + AD = BC + CDD) AB + CD = AD + BC

Answer

✓ Correct Answer: Option D

Question 10

10. In a circle of radius 5 cm, a tangent at a point P intersects a line through the centre O at point Q so that OQ = 12 cm. Length PQ is:

A) 12 cmB) $\sqrt{119} cm$C) 13 cmD) 8.5 cm

Answer

✓ Correct Answer: Option B

Question 11

11. The number of tangents that can be drawn to a circle from a point situated strictly inside the circle is:

A) 2B) 1C) InfiniteD) 0

Answer

✓ Correct Answer: Option D

Question 12

12. If two tangents inclined at an angle of $60^\circ$ are drawn to a circle of radius 3 cm, then the length of each tangent is equal to:

A) $\frac{3\sqrt{3}}{2} cm$B) 3 cmC) $3\sqrt{3} cm$D) 6 cm

Answer

✓ Correct Answer: Option C

Question 13

13. PT is a tangent at point T to a circle whose centre is O. If OP = 17 cm and OT = 8 cm, find the length of tangent PT.

A) 15 cmB) 25 cmC) 9 cmD) 12 cm

Answer

✓ Correct Answer: Option A

Question 14

14. The radii of two concentric circles are 4 cm and 5 cm. Find the length of the chord of the larger circle which is tangent to the smaller circle.

A) 3 cmB) 6 cmC) 8 cmD) 9 cm

Answer

✓ Correct Answer: Option B

Question 15

15. If the angle between two radii of a circle is $130^\circ$, then the angle between the tangents drawn at the ends of these radii is:

A) $90^\circ$B) $50^\circ$C) $40^\circ$D) $70^\circ$

Answer

✓ Correct Answer: Option B

Question 16

16. According to a key circle theorem, the lengths of two tangents drawn from an external point to a circle are:

A) Perpendicular to each otherB) Always in the ratio 2:1C) EqualD) Unequal

Answer

✓ Correct Answer: Option C

Question 17

17. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn. The length of the chord CD parallel to XY and at a distance of 8 cm from A is:

A) 8 cmB) 6 cmC) 5 cmD) 4 cm

Answer

✓ Correct Answer: Option A

Question 18

18. A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12 cm. What is the radius of the circle?

A) 7 cmB) 5 cmC) 8 cmD) 10 cm

Answer

✓ Correct Answer: Option B

Question 19

19. Two parallel lines touch the circle at points A and B respectively. If the area of the circle is $25\pi cm^2$, then the length of AB is equal to:

A) 5 cmB) 8 cmC) 12 cmD) 10 cm

Answer

✓ Correct Answer: Option D

Question 20

20. What is the angle subtended by a tangent to a circle at its point of contact with the corresponding radius?

A) $90^\circ$B) $180^\circ$C) $45^\circ$D) $60^\circ$

Answer

✓ Correct Answer: Option A

Accepted Answer

✓ Correct Answer: Option C

Grade 10 Maths: Circles Interactive Quiz

1. A tangent to a circle intersects the circle in exactly how many points?

2. A line intersecting a circle in two distinct points is called a:

3. At most, how many parallel tangents can a circle have simultaneously?

4. The common point of a tangent to a circle and the circle itself is called the:

5. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. What is the radius of the circle?

6. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^\circ$, then \angle POA is equal to:

7. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is:

8. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

9. A quadrilateral ABCD is drawn to circumscribe a circle. Which of the following relations is always true?

10. In a circle of radius 5 cm, a tangent at a point P intersects a line through the centre O at point Q so that OQ = 12 cm. Length PQ is:

11. The number of tangents that can be drawn to a circle from a point situated strictly inside the circle is:

12. If two tangents inclined at an angle of $60^\circ$ are drawn to a circle of radius 3 cm, then the length of each tangent is equal to:

13. PT is a tangent at point T to a circle whose centre is O. If OP = 17 cm and OT = 8 cm, find the length of tangent PT.

14. The radii of two concentric circles are 4 cm and 5 cm. Find the length of the chord of the larger circle which is tangent to the smaller circle.

15. If the angle between two radii of a circle is $130^\circ$, then the angle between the tangents drawn at the ends of these radii is:

16. According to a key circle theorem, the lengths of two tangents drawn from an external point to a circle are:

17. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn. The length of the chord CD parallel to XY and at a distance of 8 cm from A is:

18. A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12 cm. What is the radius of the circle?

19. Two parallel lines touch the circle at points A and B respectively. If the area of the circle is $25\pi cm^2$, then the length of AB is equal to:

20. What is the angle subtended by a tangent to a circle at its point of contact with the corresponding radius?